TY - GEN
T1 - Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth
AU - Włodarczyk, Michał
N1 - Publisher Copyright:
© Michał Włodarczyk.
PY - 2023/7/1
Y1 - 2023/7/1
N2 - In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth tw of the input graph G. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time 2O(tw) · |V(G)|, improving upon the running time 2O(tw2)·|V(G)|O(1) by Jansen, de Kroon, and Włodarczyk (STOC’21). When a tree decomposition of width tw is given, then the base of the exponent equals 2ω−1·3+1. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known 2O(tw log tw) · |V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.
AB - In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth tw of the input graph G. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time 2O(tw) · |V(G)|, improving upon the running time 2O(tw2)·|V(G)|O(1) by Jansen, de Kroon, and Włodarczyk (STOC’21). When a tree decomposition of width tw is given, then the base of the exponent equals 2ω−1·3+1. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known 2O(tw log tw) · |V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.
KW - chordal graphs
KW - fixed-parameter tractability
KW - interval graphs
KW - matroids
KW - representative families
KW - treewidth
UR - http://www.scopus.com/inward/record.url?scp=85167330379&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2023.106
DO - 10.4230/LIPIcs.ICALP.2023.106
M3 - Conference contribution
AN - SCOPUS:85167330379
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
A2 - Etessami, Kousha
A2 - Feige, Uriel
A2 - Puppis, Gabriele
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
Y2 - 10 July 2023 through 14 July 2023
ER -